1. Field of the Invention
The present invention relates to an optical scanning apparatus, and more particularly to an optical scanning apparatus for simultaneously scanning a plurality of light beams.
2. Description of the Related Art
Hitherto, an optical scanning apparatus has been known which is included in an image recording apparatus, such as a laser printer or a digital copying machine, for recording an image by scanning the surface of a photosensitive member with a light beam in accordance with image information to expose the surface of the photosensitive member to the light beam, the optical scanning apparatus being structured as shown in FIG. 9.
The optical scanning apparatus causes a light beam 14 emitted from a light emitting portion 12, such as a semiconductor laser unit, to pass through an optical system 17 comprising a collimator lens and a cylindrical lens. Then, the light beam is reflected by a mirror 24 which is moved in synchronization with rotation of a rotative polygonal mirror (hereinafter referred to as "polygonal mirror") 22 in a direction indicated by an arrow B1 shown in FIG. 9. Thus, the light beam scans a photosensitive member 28 through an imaging lens 26 so that scanning and exposure are performed along the axial direction of the photosensitive member 28 in a direction indicated by an arrow B2 shown in FIG. 9.
The image recording apparatus, such as a laser printer or a digital copying machine, incorporating the above optical scanning apparatus has been required to be capable of performing a high-speed operation and forming an image having a high quality. To meet the requirement, the following technique for simultaneously scanning a plurality of light beams has been suggested.
In Japanese Patent Examined Publication No. Hei. 1-45065, Japanese Patent Unexamined Publication No. Hei. 5-176128 and a thesis "Multi-Beam Scanning Optics by a Laser Diode Array and Interlaced Scanning" ("Optics" No. 8, Vol. 23 (August 1994)), a technique has been disclosed with which the surface of a photosensitive member is interlaced-scanned by a light emitting portion having a plurality of light emitting points which can independently be light-modulated.
The technique disclosed in Japanese Patent Examined Publication No. Hei. 1-45065 has a structure incorporating two or more light emitting points disposed at an interval .gamma.. When an imaging magnification of an imaging optical system is .beta., and the number of the light emitting points is n, an interval P of adjacent scanning lines on the surface of the photosensitive member satisfies the following relationship: EQU P=.beta..multidot..gamma./(xn+1) (1)
where x is an integer satisfying x.gtoreq.0.
An object of the technique disclosed in Japanese Patent Unexamined Publication No. Hei. 5-176128 is to solve the problem experienced with the technique disclosed in Japanese Patent Examined Publication No. Hei. 1-45065. That is, the scanning apparatus must have an excessively high mechanical accuracy. The technique has a structure incorporating n (n is an integer satisfying n.gtoreq.3) light emitting points disposed in one light emitting portion at an interval .gamma.. When an imaging magnification of an imaging optical system is .beta., I and n are relatively prime, and I is an integer satisfying 2.ltoreq.I.ltoreq.n-1, an interval P among adjacent scanning lines on the surface of the photosensitive member satisfies the following relationship: EQU P=(.beta..multidot..gamma.)/I (2)
In the thesis "Multi-Beam Scanning Optics by a Laser Diode Array and Interlaced Scanning" has disclosed a technique for satisfying conditions which must be satisfied when interlaced scanning disclosed in Japanese Patent Examined Publication No. Hei. 1-45065 and Japanese Patent Unexamined Publication No. Hei. 5-176128 is performed. In the thesis, conditions under which interlaced scanning can be performed have been disclosed.
The conditions which has been disclosed in the thesis and under which interlaced scanning can be performed will now be described with reference to FIG. 11. FIG. 11 shows a state in which the number of light emitting points is four and interlaced scanning is performed by skipping three scanning lines. In the drawing, S1 to S4 represent light beams emitted from the light emitting points.
To perform the interlaced scanning, two conditions below must be satisfied:
Condition 1: All of the scanning lines must be scanned.
Condition 2: Repetition of scanning of the same scanning line must be prevented.
In this case, interlaced scanning is performed such that n (n is an integer satisfying n.gtoreq.2) light beams are positioned in the sub-scanning direction at an interval r which is a times interval P among scanning lines. When the light beams are moved in the sub-scanning direction by b times P at each main scanning, the light beams must exist on the scanning lines. Therefore, each of a and b is a natural number. To satisfy Condition 1, the movement distance h.times.b.multidot.P of the leading end light beam S1 in the sub-scanning direction after scanning h (h is a natural number) times and the length n.times.a.multidot.P of a light beam line corresponding to the distance of movement and formed in the sub-scanning direction must be the same. Therefore, the following relationship is satisfied: EQU h.times.b.multidot.P=n.times.a.multidot.P
That is, EQU h.times.b=n.times.a (3)
Since the space between light beams is filled with a required number of scanning lines as a result of h times of scanning operations, the relationship h.multidot.P=a.multidot.P, that is, the relationship h=a is satisfied. Since the interval r of the light beams satisfies r=aP, the relationship a=r/P=h is satisfied. Therefore, h is equal to a quotient (a natural number) obtained by dividing the interval r between the light beams by the interval P between the scanning lines. That is, the following relationship is satisfied: EQU h=r/P (4)
Hereinafter, h is referred to as an interlaced period (the number of pitches in the interval r). Since h=a, the relationship b=n is satisfied in accordance with Equation (3).
Condition 2 will now be described. The scanning line which is scanned with a k-th light beam at j-th scanning is indicated as number L (j, k). L (j, k) is expressed by using n and h as follows: EQU L(j, k)=(n.multidot.j+1)+h.multidot.(k-1) (5)
where j and k are as follows:
j: a serial number which is given to each main scanning and which is an integer, and PA1 k: a serial number of a light beam which is given to a leading end light beam in the sub-scanning direction and which is a natural number of 1 to n. PA1 Condition 1: an integer satisfying n.gtoreq.2 PA1 Condition 2: P=(.beta..multidot..gamma.)/h (where .beta.=.multidot..gamma. which is derived from Equation (4)) PA1 Condition 3: an integer-satisfying h.gtoreq.1 (when h=1, adjacent scanning is performed in place of interlaced scanning) PA1 Condition 4: h and n are relatively prime PA1 Condition 5: d=n.multidot.P PA1 Condition 12: P=(.beta..multidot..gamma.)/(2.multidot.i) PA1 Condition 11: an even number satisfying n.gtoreq.4 and n=2m PA1 Condition 13: an integer satisfying i.gtoreq.2 PA1 Condition 14: i and m are relatively prime. PA1 Condition 15: d1=n.multidot.P PA1 Condition 16: d2=cP (where c is an odd number satisfying 1.ltoreq.c) PA1 Condition 16': d2=cP (where c is an odd number satisfying 1.ltoreq.c&lt;i) PA1 P=(.beta..multidot..gamma.)/(2.multidot.i)=(.beta..multidot..gamma.)/6 PA1 d2=cP=P (when c=1) PA1 P=(.beta..multidot..gamma.)/(2.multidot.i)=(.beta..multidot..gamma.)/10 PA1 d2=cP=P (when c=1)
To prevent repetition scanning of the same scanning line, numbers of scanning lines formed by light beams given arbitrary numbers k1 and k2 (.noteq.k1) must not coincide with each other in j1-th main scanning and j2-th main scanning in the same interlaced period h. That is, the following Equation (6) must be satisfied: EQU L(j1, k1).noteq.L (j2, k2) (6)
The following relationships are satisfied in accordance with Equation (5): EQU L(j1, k1)=(n.multidot.j1+1)+h.multidot.(k1-1) EQU L(j2, k2)=(n.multidot.j2+1)+h.multidot.(k2-1)
Therefore, substitution for Equation (6) and arrangement of the both sides result in n (j1-j2).noteq.h (-k1+k2). Assuming that J=j1-j2 and K=-k1+k2, the following relationship is satisfied: EQU n.multidot.J.noteq.h.multidot.K (7)
Since each of J and K is an arbitrary integer except for 0 and the minimum value of each of k1 and k2 is 1 and the maximum value is n, the maximum value of .vertline.-k1+k2.vertline. is n-1. Therefore, K satisfies the following Equation (8). EQU .vertline.K.vertline..ltoreq.n-1 (8)
Since k1.noteq.k2 at this time, K.noteq.0.
When both of J and K are positive integers, the right side h.multidot.K of Equation (7) is h.multidot.(n-1), which is an integer smaller than h.multidot.n owning to the condition expressed by Equation (8). When h and n are relatively prime, the greatest common divisor of h and n is 1 and the least common multiple is h.multidot.n. Therefore, a value n.multidot.J obtained by multiplying n with an arbitrary integer J is not equal to h.multidot.K which is an integer smaller than h.multidot.n. Therefore, Equation (7) is satisfied. Similarly, Equation (7) is also satisfied when both of J and K are negative integers. If the signs are different from each other, Equation (7) is apparently satisfied because h and n are natural numbers.
The foregoing facts are summarized such that the conditions under which interlaced scanning can be performed are expressed as follows by using the number n of light emitting points, the interval P between adjacent scanning lines on the surface of the photosensitive member and the interlaced period h:
(1) An amount of movement (an interval d between the scanning lines caused by the same light emitting point) of the same scanning line in the sub-scanning direction at each main scanning must be n.multidot.P (the condition under which all of the scanning lines are scanned).
(2) Numbers indicated by h and n must be relatively prime (the condition under which repetitive scanning can be prevented).
In summary, the conditions under which interlaced scanning can be performed are the following Conditions 1 to 5 by the imaging magnification .beta. and the interval .gamma. among light emitting points in a direction perpendicular to the main scanning direction:
When Conditions 1 to 5 are satisfied, interlaced scanning can be performed.
A portion of the conditions about the number n of light emitting points and the interlaced period h which satisfy the foregoing Conditions 1 to 5 is shown in Table 1. Note that symbol A shown in Table 1 indicates the combination of the number n of light emitting points and the interlaced period h corresponding to the technique disclosed in Japanese Patent Examined Publication No. Hei. 1-45065, B indicates the combination of the number n of light emitting points and the interlaced period h corresponding to the technique disclosed in Japanese Patent Unexamined Publication No. Hei. 5-176128, C indicates the combination of the number n of light emitting points and the interlaced period h added by the technique disclosed in the foregoing thesis ("Multi-Beam Scanning Optics by a Laser Diode Array and Interlaced Scanning") and D indicates no combination.
As shown in Table 1, when n is determined, h which can be taken is discretely determined.
TABLE 1 ______________________________________ Interlaced Number n of Light Emitting Points Period h 2 3 4 5 6 7 8 9 ______________________________________ 2 D B D B D B D B 3 A D B B D B B D 4 D A D B D B D B 5 A C A D B B B B 6 D D D A D B D D 7 A A C C A D B B 8 D C D C D A D B 9 A D A C D C A D ______________________________________
However, the technique for simultaneously scanning a plurality of light beams suffers from the following problems.
That is, the above conventional technique is structured to perform interlaced scanning to solve the problem which arises owning to the adjacent scanning. Since a plurality of light emitting points are disposed straight at the same interval on the surface of one light emitting portion, the interval among the scanning lines which are simultaneously scanned is inevitably elongated. Therefore, a larger number of line buffer memories are required as compared with execution of the adjacent scanning. If the number n of light emitting points is 4 and the interlaced period h is 5, sixteen or more line buffer memories, which are four times the number of line buffer memories required for adjacent scanning, are required. The foregoing fact will now be described with reference to FIGS. 10(A) and 10(B). In FIGS. 10(A) and 10(B), a state of writing of scanning lines at each scanning is clarified by shifting the position at which writing is started to the right at each scanning using four light beams.
As shown in FIG. 10(A), all of light beams cannot be modulated at first scanning when interlaced scanning is performed. At first scanning, the position of a fourth scanning line is scanned by a fourth light emitting point in the sub-scanning direction. Second main scanning is performed such that third and fourth light emitting points in the sub-scanning direction scan the positions of third and eighth lines. When scanning is continued similarly, all of the four light emitting points are modulated at fourth scanning. At this time, the positions of first, sixth, eleventh and sixteenth scanning lines are simultaneously scanned. Therefore, the four light beams must simultaneously be modulated. At least data of modulation at the positions from the first line to the sixteenth line must be stored in the line buffer memories. Among stored data, data of modulation for four lines must be selected so as to be input to the light emitting portions.
On the other hand, adjacent scanning permits all of the four light emitting points to be modulated from first scanning, as shown in FIG. 10(B). Therefore, the line buffer memory is required to store data of modulation for four lines.
The above conventional technique for simultaneously scanning a plurality of light beams must form all of light emitting points for simultaneously emitting light on a straight line on the surface of one light emitting portion. When the pitch of the scanning lines on the photosensitive member is required to be reduced, the interval among the light emitting points must be reduced. In this case, light emitting portions satisfying the requirement cannot easily be manufactured. That is, respective light emitting points must be provided with terminals through which electric power is supplied from a power source and which is formed by wire bonding or the like. If the interval among the light emitting points is too small, simple machining, including the wire bonding process, cannot be performed. Therefore, special machining must be performed.